Elliptic curve isogeny class with LMFDB label 8330.w (Cremona label 8330s)

• Label: 8330.w
• Number of curves: $1$
• Conductor: $8330$
• CM: no
• Rank: $0$

Rank

The elliptic curve 8330.w1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8330.w do not have complex multiplication.

Modular form 8330.2.a.w

Elliptic curves in class 8330.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8330.w1	8330s1	\([1, 0, 0, -43856, -3546880]\)	\(-79290863149681/213248000\)	\(-25088413952000\)	\([]\)	\(25344\)	\(1.4454\)	\(\Gamma_0(N)\)-optimal